The relative aging is an important notion which is useful to measure how a system ages relative to another one. Among the existing stochastic orders, there are two important orders describing the relative aging of two systems, namely, aging faster orders in the cumulative hazard and the cumulative reversed hazard rate functions. In this paper, we give some sufficient conditions under which one coherent system ages faster than another one with respect to the aforementioned stochastic orders. Further, we show that the proposed sufficient conditions are satisfied for k-out-of-n systems. Moreover, some numerical examples are given to illustrate the applications of proposed results.

中文翻译：

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相干系统与相同分布组件的相对老化比较

相对老化是一个重要的概念，它有助于衡量一个系统相对于另一个系统如何老化。在现有的随机阶中，有两个重要阶描述了两个系统的相对老化，即累积危险中的老化更快阶和累积反向危险率函数。在本文中，我们给出了一些充分条件，在这些条件下，相对于上述随机顺序，一个相干系统比另一个系统老化得更快。此外，我们证明了所提出的充分条件满足ķ-在......之外-n系统。此外，还给出了一些数值例子来说明所提出结果的应用。